Navigation

These are the slides from the August 8, 2015 Seminar.

What is navigation? This slide puts up a few possible answers. Of course every answer raises a new question. What is going from A to B? If A is here, where is here? And if B is a planet orbiting Alpha Centauri, what is our strategy for getting there?

Of course we’re not considering interstellar travel yet, at least not on this course. But I am not being flippant bringing it up. There is a technique here for thinking about things and learning. Sometimes you can profit from backing away and looking at the BIG picture. Then you narrow it down into the range in question, and a concept that seemed very difficult will suddenly make sense.

We fly airplanes in Earth’s atmosphere. The atmosphere is a thin shell around the sphere (sort of) that is Earth. Orbital mechanics and the gravitational pull of the sun and Alpha Centauri are not going to play a part in our calculations.

For short distances, we can even pretend that the earth is flat. Or maybe not. Not quite. We’ll get to that.

The first two questions on the slide are about planning. A to B. Where is A? Where is B? We have to have a way of describing our present position. My house. The button of runway 24L at Dorval. A set of lat/long co-ordinates. Likewise with B. They are both points on the surface of the globe.

OK, connect the dots. Easy, right? Just make a straight line between them. Then see which way this straight line points, relative to, let’s say, North. But what is North? Where a magnetic compass points? Where Polaris can be seen at night? What about if you are in New Zealand?

OK, I know this is getting tedious. But questions are good. They are the road to understanding.

Just before we leave this slide, consider the last bullet point: knowing where we will be. This is the most practical of all. It defines the skill we are going to develop: navigation.

But first, a bit of history. The history of navigation is relevant for two reasons:

Most of the theory we use to navigate today was developed in the era of sailing ships, before the year 1800.

Looking at snapshots from history is analogous to navigation itself

Dead Reckoning

When we zoom in on the act of navigation, at the most fine-grained level dead reckoning is what we see. Dead reckoning says, if I move in that direction at that speed for that long, I will describe that line.

The line has a direction and a length, so if I make an x on the chart where I am (or where I think I am) and dead reckon for an hour, I can draw a line on the chart from my x. At the other end of the line, I make another x. That is my new position.

Sailing ships kept logs (we keep flight logs). Every hour ships navigators would make an x on the chart. Sometime during the next hour they would “heave the log.” This consisted of a light rope with a drag on the end (like a small parachute). There were knots in the rope a certain distance apart – usually 8 fathoms, or 48 feet. A 28-second sandglass was used to time the runout of the line. The number of knots that went by was their speed in, appropriately, knots.

The helmsman would steer the same course for an hour. Then the navigator would make a new x on the chart. If they were making five knots, the new x would be five miles from the previous x.

The Sextant

The sextant is used to find the angle between a celestial body and the horizon. That angle will give a line of position. For example, the angle between the sun at noon and the horizon can yield a line of latitude.

To find longitude, we need to know what time it is. That is because we have to know what our point on the globe is looking up at. Another way of saying it is, as the earth spins on its axis, where are we relative to, for example, the sun? That’s day and night, and of course it depends on where we are on the globe. Navigators (and pilots) use the time at 0 degrees longitude, the Greenwich Meridian, to standardize the measurement of time world-wide. When the sun is directly overhead at Greenwich, it is noon Greenwich Mean Time. That time reference is known today as Coordinated Universal Time.

We can use the sextant to determine what time it is, but that takes measuring the lunar distance, the angle between the moon and a star or planet. But that option is not available during the day, hence the need for a chronometer.

Just look at your watch, right? Well, in the 18th Century it wasn’t quite that easy. Most clocks used pendulums, and those don’t work on a rolling ship at sea. So there was an incentive to develop a very accurate timepiece that used an escapement instead.

There is another complication. Ships sail the sea, which is itself in motion relative to the land, or indeed to the sea floor. In airplanes it is the same: we move through the (mostly) invisible air, which is moving over the land below. So if we fly through the air with a certain direction and speed, our progress over the ground will (if there is wind) be different from our path through the air. This is true in three dimensions – for example, if a strong downdraft exceeds the aircraft’s maximum rate of climb, the aircraft will descend.

Did you float sticks in the gutter as a kid? Did you and a friend race your sticks in the April melt?

You may have noticed that in the last few slides the background picture has been changing.

Did you see the stick? It is moving in the current. The current is from right to left at four knots. So if we want to swim to the small island, we will have to aim toward the larger island on the right.